The procedure for measuring the absolute value of \(\operatorname{tr}(P \rho )\)  requires only two-copy Bell basis measurements, which can be performed quite easily on current quantum devices [1]}, [2]}.
On the other hand, the procedure for measuring signs of \(\operatorname{tr}(P \rho )\)  can be rather difficult to implement on a near-term quantum device.
However, for measuring signs, we only need to investigate the Pauli operator expectation values found to be relatively large in absolute value. For any \(P\)  such that \(|\operatorname{tr}(P \rho )|\)  is small,
rather than determine the sign we simply set our predicted expectation value of \(P\)  to zero.
